Coherent and radiative couplings through 2D structured environments

We study coherent and radiative interactions induced among two or more quantum units, by coupling them to two-dimensional lattices acting as structured environments. This model can be representative of atoms trapped near photonic crystal slabs, trapped ions in Coulomb crystals or to surface acoustic waves on piezoelectric materials, cold atoms on state-dependent optical lattices, or even circuit QED architectures, to name a few. We compare coherent and radiative contributions for the isotropic and directional regimes of emission into the lattice, for infinite and finite lattices, highlighting their differences and existing pitfalls, e.g. related to long-time or large-lattice limits. We relate the phenomenon of directionality of emission with linear-shaped isofrequency manifolds in the dispersion relation, showing a simple way to disrupt it. For finite lattices, we study further details as the scaling of resonant number of lattice modes for the isotropic and directional regimes, and relate this behavior with known van Hove singularities in the infinite lattice limit. Further we export the understanding of emission dynamics with the decay of entanglement for two quantum, atomic or bosonic, units coupled to the 2D lattice. We analyze in some detail completely subradiant configurations of more than two atoms, which can occur in the finite lattice scenario, in contrast with the infinite lattice case. Finally we demonstrate that induced coherent interactions for dark states are zero for the finite lattice.Comment: 10 page

Completely subradiant multi-atom architectures through 2D photonic crystals

Inspired by recent advances in the manipulation of atoms trapped near 1D waveguides and pro- posals to use surface acoustic waves on piezoelectric substrates for the same purpose, we show the potential of two-dimensional platforms. We exploit the directional emission of atoms near photonic crystal slabs with square symmetry to build perfect subradiant states of 2 distant atoms, possible in 2D only for finite lattices with reflecting boundaries. We also show how to design massively parallel 1D arrays of atoms above a single crystal, useful for multi-port output of nonclassical light, by ex- ploiting destructive interference of guided resonance modes due to finite size effects. Directionality of the emission is shown to be present whenever a linear iso-frequency manifold is present in the dispersion relation of the crystal. Multi-atom radiance properties can be obtained from a simple cross-talk coefficient of a master equation, which we compare with exact atom-crystal dynamics, showing its predictive power

Anisotropic quantum emitter interactions in two-dimensional photonic-crystal baths

Quantum emitters interacting with two-dimensional photonic-crystal baths experience strong and anisotropic collective dissipation when they are spectrally tuned to 2D Van-Hove singularities. In this work, we show how to turn this dissipation into coherent dipole-dipole interactions with tuneable range by breaking the lattice degeneracy at the Van-Hove point with a superlattice geometry. Using a coupled-mode description, we show that the origin of these interactions stems from the emergence of a qubit-photon bound state which inherits the anisotropic properties of the original dissipation, and whose spatial decay can be tuned via the superlattice parameters or the detuning of the optical transition respect to the band-edges. Within that picture, we also calculate the emitter induced dynamics in an exact manner, bounding the parameter regimes where the dynamics lies within a Markovian description. As an application, we develop a four-qubit entanglement protocol exploiting the shape of the interactions. Finally, we provide a proof-of-principle example of a photonic crystal where such interactions can be obtained.Comment: 12 pages, 8 figure

Multi-ion sensing of dipolar noise sources in ion traps

Trapped-ion quantum platforms are subject to `anomalous' heating due to interactions with electric-field noise sources of nature not yet completely known. There is ample experimental evidence that this noise originates at the surfaces of the trap electrodes, and models assuming fluctuating point-like dipoles are consistent with observations, but the exact microscopic mechanisms behind anomalous heating remain undetermined. Here we show how a two-ion probe displays a transition in its dissipation properties, enabling experimental access to the mean orientation of the dipoles and the spatial extent of dipole-dipole correlations. This information can be used to test the validity of candidate microscopic models, which predict correlation lengths spanning several orders of mag- nitude. Furthermore, we propose an experiment to measure these effects with currently-available traps and techniques

Discording power of quantum evolutions

We introduce the discording power of a unitary transformation, which assesses its capability to produce quantum discord, and analyze in detail the generation of discord by relevant classes of two-qubit gates. Our measure is based on the Cartan decomposition of two-qubit unitaries and on evaluating the maximum discord achievable by a unitary upon acting on classical-classical states at fixed purity. We found that there exist gates which are perfect discorders for any value of purity, and that they belong to a class of operators that includes the $\sqrt{{SWAP}}. Other gates, even those universal for quantum computation, do not posses the same property: the CNOT, for example, is a perfect discorder only for states with low or unit purity, but not for intermediate values. The discording power of a two-qubit unitary also provides a generalization of the corresponding measure defined for entanglement to any value of the purity.Comment: accepted for publication in Physical Review Letter

Quantum Otto cycle with inner friction: finite-time and disorder effects

The concept of inner friction, by which a quantum heat engine is unable to follow adiabatically its strokes and thus dissipates useful energy, is illustrated in an exact physical model where the working substance consists of an ensemble of misaligned spins interacting with a magnetic field and performing the Otto cycle. The effect of this static disorder under a finite-time cycle gives a new perspective of the concept of inner friction under realistic settings. We investigate the efficiency and power of this engine and relate its performance to the amount of friction from misalignment and to the temperature difference between heat baths. Finally we propose an alternative experimental implementation of the cycle where the spin is encoded in the degree of polarization of photons.Comment: Published version in the Focus Issue on "Quantum Thermodynamics

Orthogonal measurements are {\it almost} sufficient for quantum discord of two qubits

The common use in literature of orthogonal measurements in obtaining quantum discord for two-qubit states is discussed and compared with more general measurements. We prove the optimality of orthogonal measurements for rank 2 states. While for rank 3 and 4 mixed states they are not optimal, we present strong numerical evidence showing that they give the correct quantum discord up to minimal corrections. Based on the connection, through purification with an ancilla, between discord and entanglement of formation (EoF), we give a tight upper bound for the EoF of a $2\otimes N$ mixed state of rank 2, given by an optimal decomposition of 2 elements. We also provide an alternative way to compute the quantum discord for two qubits based on the Bloch vectors of the state.Comment: EPL 96, 40005 (2011